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Transactions of the American Mathematical Society

Published by the American Mathematical Society since 1900, Transactions of the American Mathematical Society is devoted to longer research articles in all areas of pure and applied mathematics.

ISSN 1088-6850 (online) ISSN 0002-9947 (print)

The 2024 MCQ for Transactions of the American Mathematical Society is 1.48 .

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Enriched $P$-Partitions
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by John R. Stembridge
Trans. Amer. Math. Soc. 349 (1997), 763-788
DOI: https://doi.org/10.1090/S0002-9947-97-01804-7

Abstract:

An (ordinary) $P$-partition is an order-preserving map from a partially ordered set to a chain, with special rules specifying where equal values may occur. Examples include number-theoretic partitions (ordered and unordered, strict or unrestricted), plane partitions, and the semistandard tableaux associated with Schur’s $S$-functions. In this paper, we introduce and develop a theory of enriched $P$-partitions; like ordinary $P$-partitions, these are order-preserving maps from posets to chains, but with different rules governing the occurrence of equal values. The principal examples of enriched $P$-partitions given here are the tableaux associated with Schur’s $Q$-functions. In a sequel to this paper, further applications related to commutation monoids and reduced words in Coxeter groups will be presented.
References
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Bibliographic Information
  • John R. Stembridge
  • Affiliation: Department of Mathematics, University of Michigan, Ann Arbor, Michigan 48109–1109
  • Received by editor(s): August 25, 1994
  • Additional Notes: Partially supported by NSF Grants DMS–9057192 and DMS–9401575
  • © Copyright 1997 American Mathematical Society
  • Journal: Trans. Amer. Math. Soc. 349 (1997), 763-788
  • MSC (1991): Primary {06A07, 05E05}
  • DOI: https://doi.org/10.1090/S0002-9947-97-01804-7
  • MathSciNet review: 1389788